Part of the reason backwards sounds more familiar than forwards is due to the number of idioms that use ”backwards" such as "Backwards about coming forward" and "Bend over backwards".
In British English, forward and backward are adjectives, whereas forwards and backwards are adverbs. The Chicago Manual of Style says,
"The preferred form in American English is toward: this has been so since about 1900. In British English, towards predominates. The same is true for other directional words, such as upward, downward, forward, and backward, as well as afterward. The use of afterwards and backwards as adverbs is neither rare nor incorrect (and is preferred in British English). For the sake of consistency, many American editors prefer the shorter forms without the final s."